Advanced mirror concepts for high-precision metrology [Elektronische Ressource] / Frank Brückner. Gutachter: Andreas Tünnermann ; Ulf Peschel ; Chang-Hasnain

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• Physik

Informations

• Publié par: friedrich-schiller-universitat_jena
• Publié le: 01 janvier 2011
• Nombre de lectures: 59
• Poids de l'ouvrage: 26 Mo

Extrait

Advanced mirror concepts for
high-precision metrology
DISSERTATION
zur Erlangung des akademischen Grades
doctor rerum naturalium
{ Dr. rer. nat. {
vorgelegt dem Rat der Physikalisch-Astronomischen Fakult at
der Friedrich-Schiller-Universit at Jena
von Diplom-Physiker Frank Bruc kner
geboren am 21.08.1981 in DresdenGutachter
1. Prof. Dr. Andreas Tunnermann, Friedrich-Schiller-Universitat Jena
2. Prof. Dr. UlfPeschel, Friedrich-Alexander-UniversitatErlangen-Nurn berg
3. Prof. Dr. Connie Chang-Hasnain, University of California, Berkeley
Tag der Disputation: 08.02.2011Contents
Table of contents I
1 Introduction 1
2 The current state of knowledge 4
2.1 Thermal noise in high-precision metrology . . . . . . . . . . . . . . . . . . 4
2.2 Brownian thermal noise due to dielectric optical coatings . . . . . . . . . . 7
2.3 Guided-mode resonant waveguide gratings (RWGs) . . . . . . . . . . . . . 12
2.3.1 Description of RWGs in a ray picture . . . . . . . . . . . . . . . . . 14
2.3.2 of RWGs by the modal method . . . . . . . . . . . . . 20
2.3.3 Rigorous numerical treatment of RWGs . . . . . . . . . . . . . . . . 26
3 RWGs for mirror applications 29
3.1 Tantala based RWGs for 1064 nm laser light . . . . . . . . . . . . . . . . . 30
3.1.1 Grating design considerations . . . . . . . . . . . . . . . . . . . . . 30
3.1.2 Fabrication process . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.3 Experimental characterization . . . . . . . . . . . . . . . . . . . . . 32
3.1.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Silicon based RWGs for 1550 nm laser light . . . . . . . . . . . . . . . . . . 35
3.2.1 Grating design considerations . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Fabrication process . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.3 Experimental characterization . . . . . . . . . . . . . . . . . . . . . 42
3.2.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . 44
IContents II
4 New approach for monolithic RWGs I - T-shaped grating 46
4.1 Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 T-shaped grating in silicon for 1550 nm laser light . . . . . . . . . . . . . . 50
4.2.1 Grating design considerations . . . . . . . . . . . . . . . . . . . . . 50
4.2.2 Fabrication process . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.3 Experimental characterization . . . . . . . . . . . . . . . . . . . . . 56
4.2.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 T-shaped grating in lithium niobate for 1064 nm laser light . . . . . . . . . 60
4.3.1 Grating design considerations . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Prospects for the fabrication process . . . . . . . . . . . . . . . . . 64
5 New approach for monolithic RWGs II - Encapsulated grating 67
5.1 Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Encapsulated grating in silicon for 1550 nm laser light . . . . . . . . . . . . 70
5.2.1 Grating design considerations . . . . . . . . . . . . . . . . . . . . . 70
5.2.2 Fabrication process . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.3 Experimental characterization . . . . . . . . . . . . . . . . . . . . . 74
5.2.4 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3 Encapsulated grating in fused silica . . . . . . . . . . . . . . . . . . . . . . 76
5.3.1 Design considerations for a narrowband tunable NIR bandstop lter 76
5.3.2 Prospects for the fabrication process . . . . . . . . . . . . . . . . . 79
6 Conclusions and outlook 81
Bibliography 86
Acknowledgements 97
Zusammenfassung 99
Publications in peer-reviewed journals 102
Conference contributions 1051 Introduction
In fundamental physics increased research activity is currently taking place on opto-
mechanical systems in which a light eld is coupled via radiation pressure to the dynamics
of a mechanical oscillator [1{6]. The surface of the mechanical device provides the interface
between the light eld and the solid state matter. Opto-mechanical coupling is widely
realized by setting up linear Fabry-Perot resonators with the cavity mirrors being the
key object of observation. In particular, cavity mirrors for laser radiation are essential as
heavy test masses of space-time for the new eld of gravitational wave astronomy [6, 7],
as mechanical oscillators for targeting the quantum regime of macroscopic mechanical
devices [4, 8{10], and for ultra-high-precision optical clocks designed for researching the
nature of fundamental constants [11{14]. Current limitations in such elds are set by the
general problem of lacking appropriate cavity mirror qualities.
The purpose of cavity mirrors is to repeatedly retro-re ect laser light such that it con-
structively interferes with the stored cavity eld, yielding maximum eld amplitudes and
providing an output eld of highest phase stability. This requires for cavity mirrors with
high re ectivity and a geometrically well de ned surface pro le. If the mirror surface
shows statistical uctuations, for example driven by Brownian motion of the mirror’s
molecules, the phase fronts of subsequently re ected waves are slightly di erent and can-
not perfectly interfere constructively. This results in a reduced cavity buildup and, in the
most severe cases, in changes of the phase of the output laser beam. Any motion of the
mirror surfaces, driven by thermal energy, is known as (Brownian) thermal noise and is
currently a major limiting factor in many research elds targeting fundamental questions
of nature as mentioned above [15{17].
The best starting point for the fabrication of low thermal noise mirrors is to employ materi-
als such as fused silica or silicon with high intrinsic mechanical quality factors (Q-factors),
1CHAPTER 1. INTRODUCTION 2
low thermal expansion coe cients and low absorption of the laser light at cryogenic tem-
peratures. A useful summary of thermal noise relations can be found in Ref. [18]. In
order to achieve high re ectivities for high- nesse setups, dielectric multilayer coatings
on the substrate’s surface are currently employed and re ectivities up to 99.9998 % have
been demonstrated [19]. Typical coating layer materials are SiO and Ta O . These two2 2 5
materials show very low optical absorption at the prominent laser wavelength of 1064 nm
where ultrastable solid state continuous wave laser sources exist [20], and are therefore
frequently used in high-precision experiments. However, recent theoretical and experi-
mental research revealed that these coatings reduce the substrate Q-factors and, most
severely, lead to a strong inhomogeneous dissipation and therefore to a rapidly increasing
Brownian thermal noise level [15,21{24].
Thus, new concepts are required that simultaneously provide high optical quality and low
mechanical loss. One approach being pursued is to design an alternative multilayer sys-
tem deviating from the classical quarter wave design and containing less Ta O [25] which2 5
causes the major loss contribution [26]. Doping of Ta O with TiO has also been investi-2 5 2
gated and a reduction of the mechanical loss by a factor of 1.5 was observed [27]. Besides
optimizing multilayer stacks [25{27] or trading o coherent thermal noise sources [17,28],
coating reduced or possibly coating free (i.e. monolithic) mirror concepts are of enormous
interest. Previous published approaches, such as corner re ectors [29{31] or whispering
gallery mode resonators [32,33], are based on total internal re ection and signi cant op-
tical path lengths inside a substrate giving rise to absorption and thermorefractive noise
resulting from a temperature dependent index of refraction.
In this thesis the capability of so called surface relief guided-mode resonant waveguide grat-
ings (RWGs) [34{37] is investigated to provide a solution for the demands mentioned
above. Such gratings represent a completely alternative approach for reaching high re-
ectivity and simultaneously ensure low mechanical loss. The coating thermal noise is
reduced due to the fact that the (high mechanical quality) substrate carries only a thin
single but corrugated high refractive index layer. A coating related reduction of substrate
Q-factors should also be greatly avoided as suggested by rst experimental results [24].
The focus of earlier work on waveguide grating structures was centered mainly on narrow-
band ltering and switching applications [35]. However, Bunkowski et al. [38] theoreticallyCHAPTER 1. INTRODUCTION 3
investigated such a device, found parameters for a high-re ection waveguide mirror with
broad spectral response, and rst proposed to use RWGs instead of conventionally coated
mirrors for applications as mentioned above.
The second chapter of this thesis will introduce in more detail the origin and character-
istics of coating related thermal noise as well as theoretical basics for the treatment of
RWGs in a ray picture and by modal methods, respectively. Based on this, the third
chapter shows the experimental realization of nonmonolithic RWGs for tantala supported
(working at a 1064 nm wavelength) [39] as well as silicon supported (working at a 1550 nm
wavelength) con gurations. The latter has been considered because within the past few
years silicon rather than fused silic